Question

solve quadratics quiz
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
1 essay 1 point
solve the following quadratic by factoring:
$2x^2 - 5x - 3$

Explanation:

Step1: Split middle term

Rewrite $-5x$ as $x - 6x$:
$2x^2 + x - 6x - 3$

Step2: Group and factor pairs

Group terms and factor GCFs:
$x(2x + 1) - 3(2x + 1)$

Step3: Factor out common binomial

Extract $(2x + 1)$ from both terms:
$(2x + 1)(x - 3)$

Step4: Solve for $x$

Set each factor equal to 0:
$2x + 1 = 0 \implies x = -\frac{1}{2}$
$x - 3 = 0 \implies x = 3$

Answer:

The factored form is $(2x + 1)(x - 3)$, and the solutions are $x = -\frac{1}{2}$ and $x = 3$.